It was not clear whether Ms. Pirro was planning to use the book she already has in the works, tentatively titled “Liars, Leakers and Liberals,” as a vehicle. That book is due out June 12 from Center Street, an imprint of the publishing giant Hachette.
Ms. Pirro, in a statement on Saturday provided by Fox News, said: “My upcoming book is not a direct response to ‘Fire and Fury.’ The title on Amazon always has been and continues to be ‘Liars, Leakers and Liberals’ and I plan to cover all of them.”
But inside the White House, Ms. Pirro is believed to have pitched her book to Mr. Trump as a plum opportunity to present a counterpoint to Mr. Wolff. And she has broadly discussed with friends the idea of a book to rebut “Fire and Fury.”
White House aides declined to comment.
Ms. Pirro, a former Westchester County district attorney, has not been shy about her newfound proximity to power. On Wednesday, she tweeted a photograph of herself standing by the White House gates.
“Guess where I am?” she wrote.
Ms. Pirro, who shares Mr. Trump’s love of showmanship, has publicly denounced the attorney general, Jeff Sessions, and the special counsel, Robert S. Mueller III. She delivered a fiery monologue in December on her weekend Fox News program, “Justice With Judge Jeanine,” in which she called for F.B.I. and Justice Department officials “to be taken out in cuffs.”
But she has pressed her case in private, too, including at an Oval Office meeting with the president in November during which she castigated Mr. Sessions and accused the former F.B.I. director James B. Comey of Mafia-style behavior. (The president’s chief of staff, John F. Kelly, interrupted Ms. Pirro and told her that she was not “helping things.”)
Ms. Pirro’s book will have to compete in a crowded Trump publishing marketplace.
Sean Spicer, the former White House press secretary, is releasing an account of his rocky tenure, “The Briefing,” in July. “Under Fire: Reporting From the Front Lines of the Trump White House,” by the Washington correspondent April D. Ryan, is due in September. Mr. Comey’s memoir, “A Higher Loyalty: Truth, Lies and Leadership,” will be released in April.
A spokeswoman for Hachette did not respond to an inquiry on Saturday. On its website, the publishing house describes “Liars, Leakers and Liberals” as “Judge Jeanine’s no-holds-barred answer to fake news.” A promotional page says that Ms. Pirro plans to interview Ivanka Trump, the president’s daughter and adviser, and to defend Mr. Trump against the news media, which “has twisted his words to fit the narrative they’ve created.”
Center Street, Ms. Pirro’s imprint, is a popular platform for conservatives and allies of Mr. Trump. It published “Let Trump Be Trump,” by the Trump loyalists Corey Lewandowski and David Bossie, last year.
In March, Center Street will release “Understanding Trump,” an account of the president by Newt Gingrich that includes a foreword by the president’s son Eric. The book features an endorsement on its cover from Ms. Pirro’s colleague at Fox News, Sean Hannity, who calls it “inspiring and informative.”